Recent advancement of measurement techniques in the biomedical field has enabled the researchers to make a considerable number of findings in proteins, cells, and organs. From the viewpoint of measurement, proteins, cells, and organs are distinct objects with different relative scales. One measurement technique is only applicable to the objects within a particular scale range, and so are the findings of the measurement. This means that the measurement-based approach is not capable enough for the researchers to make a satisfactory finding in the study field of, for example, interactive behavior of cells and organs. The difficulty comes from the large difference in scale between the cells and organs.
The computer technology, on the other hand, have evolved rapidly toward ever higher performance, and computer simulation takes advantage of such performance enhancements. Simulation-based research has been increasingly used to compensate for the lack of findings in the study that deals with objects in different scales (e.g., large objects in combination with small objects). This approach appears to be leading to new discoveries which could not have been achieved by the conventional measurement-based or experiment-based study.
Computer simulation is used in research of the heart, one of the most popular organs as a subject of study. The heart is an important organ that sends out blood to the entire body, where the blood circulation is one of the most fundamental mechanisms of life. It is noted that the heart itself also needs a stable supply of blood. Delivery of blood to the heart is done via a set of vessels known as the coronary circulatory system. Pathological conditions derived from abnormalities in the coronary circulation are collectively referred to as ischemic heart diseases.
Ischemic heart diseases are mainly caused as a result of coronary arteriosclerosis. Most studies about arteriosclerosis are made from the viewpoint of the biochemistry and cell biology. The pathogenesis of ischemic heart diseases is closely related to functional factors such as structure and control of the coronary circulatory system. For example, the heart contraction is considered to give a strong effect on the coronary blood flow. It is known that, with the presence of angina pectoris, ischemia is likely to occur at the endocardial (heart chamber) side of the heart wall, where the tissue pressure increases most significantly. The tissue pressure can be estimated by using a mechanics analysis tool. Observation of blood flow (shear stress) related to atheroma formation is also important in identifying the pathogenesis of ischemic heart diseases. The mechanics analysis also works well for this blood flow observation. As can be seen, the mechanics analysis plays an important role in study of the pathogenesis of ischemic heart diseases.
Such hemodynamics peculiar to the coronary circulation has drawn the interest of researchers including those who engaged in the basic medical sciences. They have made various kinds of experimental research and have accumulated many findings. There still remain, however, a lot of unknown things about the heart because of its complexity in structure and muscular motion. For example, the coronary system includes a wide range of vessels, from trunks to capillaries, on the order of mm to μm in diameter. That is, the largest coronary vessels are about 1,000 times as wide as the smallest coronary vessels. In addition, the heart repeats contraction and relaxation to make a large motion of strokes, which adds constraints to realtime observation of coronary blood vessels. These facts hamper the investigation of hemodynamics inside the heart wall. Computer simulation with a coronary circulation model is one way to overcome such technical difficulties in the physical observation of coronary vessels. This indeed is a powerful tool to illuminate the mechanisms of the heart.
Databases for coronary circulation simulation are available today to provide detailed measurement data about, for example, the diameter and length of coronary arteries, veins, and capillaries, as well as the information describing how the vessels branch out. With such databases, various simulation methods have been proposed and discussed as listed below. A coronary circulation simulation includes computation for solving simultaneous linear equations by using a parallel iterative method. For example, a preconditioner for parallel interactive sover is proposed to overcome the ill-conditioned problem caused by widely ranging vessel diameters in the coronary circulatory system and to ensure the convergence of iteration.
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The existing simulation techniques are, however, unable to analyze the dynamics of a circulatory system that not only involves a wide range of vessels, from coronary arteries and veins to capillaries, but also incorporates the motion of heartbeats. The main reason is that the modeling of capillaries, if done faithfully, would produce too large amount of data for the simulator to finish its job within a practical time. One way to circumvent the noted problem is to use a porous medium as a substitute for the capillary-level vessels. This conventional solution, however, sacrifices the ability to analyze the pressure drops in capillaries, effect of a microcirculation structure on the coronary blood flow, or interaction between metabolism and microcirculation. Here the term “metabolism” refers to a process in myocardial cells that consumes oxygen and nutrition delivered by the capillary blood flow to produce adenosine triphosphate (ATP) for energizing the cells.
The above-noted difficulties in the simulation of coronary circulation may also be true with other organs than the heart because their blood flow varies in synchronization with their motions. This means that the noted difficulties in the dynamics analysis of a circulatory system similarly apply to the conventional simulation of other organs because of the variety of vessels from trunks to capillaries and the effect of their motions on the vessels.